How to right-justify UILabel text?

myLabel.textAlignment = UITextAlignmentRight;

iOS Developer Library is a good resource.

You should set text alignment to justified and set attributed string base writing direction to RightToLeft:

var label: UILabel = ...
var text: NSMutableAttributedString = ...
var paragraphStyle: NSMutableParagraphStyle = NSParagraphStyle.defaultParagraphStyle().mutableCopy() as! NSMutableParagraphStyle
paragraphStyle.alignment = NSTextAlignment.Justified
paragraphStyle.lineBreakMode = NSLineBreakMode.ByWordWrapping
paragraphStyle.baseWritingDirection = NSWritingDirection.RightToLeft
text.addAttribute(NSParagraphStyleAttributeName, value: paragraphStyle, range: NSMakeRange(0, text.length))
label.attributedText = text